Radio waves arriving from a transmitting antenna on radio wave propagation paths in mobile communication are reflected and scattered by the surrounding geographical features and arrive at the receiver as the assemblage of a group of element waves. As a result, the phenomenon of fading produced as a result of these factors has always been an obstacle to achieving mobile communication with high quality. The control of the degraded radio wave propagation environment resulting from this fading has been the long-standing goal of researchers in the field of mobile communication, and a wide variety of measures have been put to practical use.
In recent years, there is an active trend toward viewing the phenomenon of fading not as an enemy, but rather as an environmental resource with a hidden potential inherent in radio wave propagation in mobile communication (for example, refer to Non-Patent Documents 1 and 2).
There has further been an active move in recent years for using the dependence on spatial position in fading fluctuation referred to as Multi-USER Diversity to utilize environmental resources inherent in radio wave propagation paths, and this can also be considered a similar trend.
The above-mentioned Non-Patent Documents 1 and 2 disclose a space transmission process called BLAST (Bell Labs Layered Spatial and Temporal) for effectively utilizing signals that have undergone space-multiplex processing as a means of applying the inherent propagation resources. A means referred to as V-BLAST has been disclosed in which linear filtering and an interference canceller are combined as the architecture for realizing the space multiplex separation of this BLAST with a low level of complexity.
ZF (Zero-Forcing) standards for suppressing (nulling) the interference component or a minimum mean square error (MMSE) standard are typically used as the linear filtering.
An MP (Moore-Penrose) typical inverse matrix is known as a linear transformation for realizing nulling according to the ZF standard, and in order to improve the characteristics of the interference canceller, an ordering process is carried out by simplified estimation for realizing detection in the order of higher SNR (Signal-to-Noise Ratio) after detection. As an operation for carrying out this ordering of symbols, one known method involves the preferential use of column vectors having the smallest norm corresponding to weighting vectors of the MP typical inverse matrix.
Alternatively, a method by means of QR decomposition provides a still lower level of complexity. More specifically, QR decomposition of communication path matrix H yields H=Q·R, following which the relation:QH·Y=R·X+QH·v 
is realized between the transmitting antenna signal vector of the nT dimension:XεCnT×1 and the receiving antenna signal vector of the nR dimension:YεCnR×1 
In this case:QεCnR×nR is a unitary matrix;RεCnR×nT is an upper triangular matrix; and noise component vector:vεCnR×1 is subjected to unitary transformation, whereby transformation is realized while maintaining the separation between signals without intensifying noise.
A step process can be realized by which vectors in a matrix can be reordered to allow processing in the order of higher SNR in the QR decomposition process for detecting in an order in which the SNR has been maximized. This type of method corresponds to a nulling process by means of the ZF standard and assumes that the number nR of receiving antennas is the same as or greater than the number of transmitting antennas nT.
However, the defect of these methods is that nT−1-order null generation is carried out in linear processing by nulling in the initial step, whereby the diversity gain can only obtain the order of:nR−nT+1.
Accordingly, detection errors tend to occur in the initial step, and the effect of these errors results in the occurrence of the propagation of error that causes detection errors in later stages.
However, optimized detection calls for MLD (Maximum Likelihood Decoding) in the equation:
      X    MLD    =      arg    ⁢                  ⁢                  min                  X          ∈                                                  A                                                    n              T                                          ⁢                                              Y            -                          H              ·              X                                                2            
As a result, the number of antennas and the size A of the modulated signal points:A=|A|produces an exponential increase in the level of complexity, and when encoding is taken into consideration, MLD becomes impossible in actuality.
Methods based on the turbo principle are therefore being investigated as methods of lowered complexity. The above-described equation is the MLD for only a detector, and the application of a decoding method known as “SD (Sphere Decoding)” is being proposed for the purpose of avoiding this degree of complexity and obtaining diversity gain in the degradation of characteristics caused by the propagation of errors from an initial stage to later stages in the above-described V-BLAST, in other words, in a fading environment.
As the basic concept of SD, a likelihood calculation is carried out for signal points that are contained in a sphere of appropriate radius r that centers on the received signal points, whereby MLD is carried out within a limited range, and as a result, efficiency is determined by the method of selecting radius r. Alternatively, a method also exists in which a degree of complexity is avoided by limiting the number of signal points according to the size of likelihood.
Non-Patent Document 1: “Layered spatial and temporal architecture for wireless communications in a fading environment when using multiple antennas” (1996, Bell Labs Technical Journal, Volume 6, Number 2, pp. 41-59).
Non-Patent Document 2: “Capacity of multi-antenna Gaussian channels” (November/December 1999, European Transactions on Telecommunication, pp. 585-595)